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2015 Picard groups and torsion-free cancellation for orders in $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$
Ryan Karr
Rocky Mountain J. Math. 45(6): 1873-1886 (2015). DOI: 10.1216/RMJ-2015-45-6-1873

Abstract

We examine the question of direct-sum cancellation of finitely generated, torsion-free modules over ring orders $R$ contained in $\mathbb{Z} \oplus \mathbb{Z} \oplus \mathbb{Z}$. Using conditions involving the Picard group and the unit group of $R$, we give a nearly complete classification of those orders $R$ for which torsion-free cancellation holds. There is exactly one `exceptional' order to which our methods do not apply.

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Ryan Karr. "Picard groups and torsion-free cancellation for orders in $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$." Rocky Mountain J. Math. 45 (6) 1873 - 1886, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1873

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1366.13007
MathSciNet: MR3473159
Digital Object Identifier: 10.1216/RMJ-2015-45-6-1873

Subjects:
Primary: 13C05, 13C20

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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